Damping materials, i.e., materials which repeatedly dissipate energy when deformed, are used in numerous applications. They may be used, for example, to mitigate vibrations, e.g., in aircraft airframes, to absorb sound, e.g., in automobiles, or to cushion impacts. It may be desirable, as in these examples, for the damping material to provide significant damping without adding more mass than necessary to the structure in which it is used. Since the damping efficiency depends on the product of the damping coefficient and the modulus, a material with high stiffness is desirable. Thus, there is a need for a lightweight material with high stiffness, and which repeatedly absorbs mechanical energy when deformed.